10K seed resazurin metabolic rate analysis
AS Huffmyer
2024
Interpretations tl;dr: - Temperature hardened oysters show less metabolic plasticity and died more under stress - Metabolic rates are different in stressed oysters - Metabolic rates are different in those that died vs those that survived under stress - We can measure changes in metabolism using resazurin assay
Set up
Set up workspace, set options, and load required packages.
knitr::opts_chunk$set(echo = TRUE, warning = FALSE, message = FALSE)Load libraries.
library(MASS)
library(tidyverse)
library(ggplot2)
library(readxl)
library(cowplot)
library(lme4)
library(lmerTest)
library(car)
library(effects)
library(emmeans)Load data
Read in resazurin data
#read in files
data <- read_csv("data/resazurin/resazurin_data.csv")
data<-data%>%
pivot_longer(names_to="time", values_to="fluorescence", cols=`0`:`4`)%>%
mutate(time=as.numeric(time))Read in survival data
surv<-read_excel("data/survival/survival_resazurin.xlsx")
surv<-surv%>%
pivot_longer(names_to="time", values_to="status", cols=`0`:`24`)%>%
mutate(time=as.numeric(time))%>%
rename(date=date.resazurin, sample=oyster)%>%
mutate(sample=as.character(sample))Read in size data
size <- read_csv("data/resazurin/resazurin-size.csv")%>%select(!notes)%>%mutate(sample=as.character(sample))Combine data
data<-left_join(data, surv)
data<-left_join(data,size)Add in final mortality status
final<-surv%>%
filter(time==24)%>%
rename(final.mortality=status)%>%
select(!time)
data<-left_join(data, final)We now have resazurin and survival data in the data frame.
data<-data%>%
mutate(final.mortality = case_when(
final.mortality == 0 ~ "alive",
final.mortality == 1 ~ "dead",
TRUE ~ as.character(final.mortality) # To handle any other values
))Data preparation
Plot the data.
data%>%
ggplot(aes(x=time, y=fluorescence, colour=temperature, group=sample))+
facet_wrap(~bag*date)+
geom_point()+
geom_line()+
theme_classic()
Calculate fluorescence at each time point normalized to the starting value at time 0.
data<-data%>%
group_by(date, bag, sample, width.mm, length.mm)%>%
arrange(date, bag, sample)%>%
mutate(fluorescence.norm=fluorescence/first(fluorescence))Plot again
data%>%
ggplot(aes(x=time, y=fluorescence.norm, colour=temperature, group=sample))+
facet_wrap(~bag*date)+
geom_point()+
geom_line()+
theme_classic()
View blanks
data%>%
filter(type=="blank")%>%
ggplot(aes(x=time, y=fluorescence.norm, colour=temperature, group=sample))+
facet_wrap(~bag*date)+
geom_point()+
geom_line()+
theme_classic()
Calculate mean change in blank at each time point.
blanks<-data%>%
filter(type=="blank")%>%
group_by(date, bag, temperature, time)%>%
summarise(mean_blank=mean(fluorescence.norm))View summarized blank data.
blanks%>%
ggplot(aes(x=time, y=mean_blank, colour=temperature))+
facet_wrap(~bag*date)+
geom_point()+
geom_line()+
theme_classic()
Subtract blank values from fluorescence values for oysters.
data<-left_join(data, blanks)
data<-data%>%
filter(!type=="blank")%>%
mutate(value=fluorescence.norm-mean_blank)Plot again.
data%>%
ggplot(aes(x=time, y=value, colour=temperature, group=sample))+
facet_wrap(~bag*date*hardening)+
geom_point()+
geom_line()+
theme_classic()
Remove unnecessary columns.
data<-data%>%
select(!type)%>%
select(!fluorescence.norm)%>%
select(!mean_blank)%>%
select(!fluorescence)Normalize blank corrected fluorescence to oyster size by dividing fluorescence value (normalized to starting value and blank corrected) by oyster size. Calculate volume by using length and width.
data$volume.mm3<-(4/3) * pi * ((data$length.mm/2) * (data$width.mm/2))^2
data$value.mm3<-data$value/data$volume.mm3Plot size normalized resazurin response.
data%>%
ggplot(aes(x=time, y=value.mm3, colour=temperature, group=sample))+
facet_wrap(~bag*date*hardening)+
geom_point()+
geom_line()+
theme_classic()
Plot against final mortality.
data%>%
filter(time==4)%>%
filter(temperature=="42C")%>%
ggplot(aes(x=final.mortality, y=value.mm3, colour=final.mortality))+
geom_point()+
theme_classic()
data%>%
filter(time==4)%>%
filter(temperature=="18C")%>%
ggplot(aes(x=final.mortality, y=value.mm3, colour=final.mortality))+
geom_point()+
theme_classic()
Under temperature stress, there appears to be a positive relationship between fluorescence at 4 hrs and final mortality status. This does not appear to show up at 18°C.
Plot size and mortality relationships.
data%>%
filter(time==4)%>%
ggplot(aes(x=volume.mm3, y=final.mortality, colour=final.mortality))+
geom_violin()+
theme_classic()
Not much difference if any.
Set time as a factor.
data$time<-as.factor(data$time)Analysis
Examine size effects
View size range.
hist(data$volume.mm3)
Remove the two outlier oysters.
data<-data%>%
filter(volume.mm3<150000)
hist(data$volume.mm3)
View metabolic rates over time as a function of size and temperature treatment using the non-size normalized fluorescence values. Include repeated measures for each individual.
model.size<-lmer(sqrt(value) ~ time * temperature * scale(volume.mm3) + (1|bag) + (1|date:bag:sample), data=data)
summary(model.size)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(value) ~ time * temperature * scale(volume.mm3) + (1 | bag) +
## (1 | date:bag:sample)
## Data: data
##
## REML criterion at convergence: 1469
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0114 -0.5143 0.0249 0.5714 3.0118
##
## Random effects:
## Groups Name Variance Std.Dev.
## date:bag:sample (Intercept) 0.11279 0.3358
## bag (Intercept) 0.01934 0.1391
## Residual 0.07001 0.2646
## Number of obs: 2190, groups: date:bag:sample, 438; bag, 10
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 6.625e-03 5.350e-02 1.455e+01 0.124
## time1 7.467e-01 2.637e-02 1.736e+03 28.318
## time2 1.289e+00 2.637e-02 1.736e+03 48.888
## time3 1.711e+00 2.637e-02 1.736e+03 64.878
## time4 2.051e+00 2.637e-02 1.736e+03 77.788
## temperature42C -3.693e-03 4.239e-02 8.419e+02 -0.087
## scale(volume.mm3) 3.612e-03 3.424e-02 8.305e+02 0.106
## time1:temperature42C 1.656e-01 3.703e-02 1.736e+03 4.471
## time2:temperature42C -1.022e-01 3.703e-02 1.736e+03 -2.759
## time3:temperature42C -3.301e-01 3.703e-02 1.736e+03 -8.914
## time4:temperature42C -5.191e-01 3.703e-02 1.736e+03 -14.018
## time1:scale(volume.mm3) 5.468e-02 2.939e-02 1.736e+03 1.860
## time2:scale(volume.mm3) 1.008e-01 2.939e-02 1.736e+03 3.431
## time3:scale(volume.mm3) 1.676e-01 2.939e-02 1.736e+03 5.704
## time4:scale(volume.mm3) 1.914e-01 2.939e-02 1.736e+03 6.512
## temperature42C:scale(volume.mm3) 5.911e-03 4.338e-02 8.409e+02 0.136
## time1:temperature42C:scale(volume.mm3) 5.321e-02 3.781e-02 1.736e+03 1.407
## time2:temperature42C:scale(volume.mm3) 1.715e-02 3.781e-02 1.736e+03 0.453
## time3:temperature42C:scale(volume.mm3) -3.717e-02 3.781e-02 1.736e+03 -0.983
## time4:temperature42C:scale(volume.mm3) -5.499e-02 3.781e-02 1.736e+03 -1.454
## Pr(>|t|)
## (Intercept) 0.903140
## time1 < 2e-16 ***
## time2 < 2e-16 ***
## time3 < 2e-16 ***
## time4 < 2e-16 ***
## temperature42C 0.930607
## scale(volume.mm3) 0.915995
## time1:temperature42C 8.30e-06 ***
## time2:temperature42C 0.005861 **
## time3:temperature42C < 2e-16 ***
## time4:temperature42C < 2e-16 ***
## time1:scale(volume.mm3) 0.062998 .
## time2:scale(volume.mm3) 0.000616 ***
## time3:scale(volume.mm3) 1.37e-08 ***
## time4:scale(volume.mm3) 9.70e-11 ***
## temperature42C:scale(volume.mm3) 0.891650
## time1:temperature42C:scale(volume.mm3) 0.159565
## time2:temperature42C:scale(volume.mm3) 0.650298
## time3:temperature42C:scale(volume.mm3) 0.325815
## time4:temperature42C:scale(volume.mm3) 0.146035
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(model.size)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value
## time 807.56 201.890 4 1736.00 2883.8631
## temperature 1.45 1.451 1 425.66 20.7208
## scale(volume.mm3) 2.28 2.279 1 432.84 32.5475
## time:temperature 29.90 7.474 4 1736.00 106.7574
## time:scale(volume.mm3) 6.63 1.657 4 1736.00 23.6748
## temperature:scale(volume.mm3) 0.00 0.000 1 426.51 0.0018
## time:temperature:scale(volume.mm3) 0.73 0.182 4 1736.00 2.6001
## Pr(>F)
## time < 2.2e-16 ***
## temperature 6.944e-06 ***
## scale(volume.mm3) 2.159e-08 ***
## time:temperature < 2.2e-16 ***
## time:scale(volume.mm3) < 2.2e-16 ***
## temperature:scale(volume.mm3) 0.96586
## time:temperature:scale(volume.mm3) 0.03456 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1rand(model.size)## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## sqrt(value) ~ time + temperature + scale(volume.mm3) + (1 | bag) + (1 | date:bag:sample) + time:temperature + time:scale(volume.mm3) + temperature:scale(volume.mm3) + time:temperature:scale(volume.mm3)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 23 -734.50 1515.0
## (1 | bag) 22 -751.84 1547.7 34.69 1 3.874e-09 ***
## (1 | date:bag:sample) 22 -1292.12 2628.2 1115.24 1 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1qqPlot(residuals(model.size))
## [1] 1046 1026plot(Effect(c("volume.mm3"), model.size))
There is a significant effect of time and size as well as interactions between time-temperature, time-size, and time-temperature-size. This indicates that metabolic scaling is different between temperatures.
Plot metabolic rates (y) over time (x) with a gradient of color for size.
data%>%
ggplot(aes(x=time, y=sqrt(value), colour=scale(volume.mm3), group=paste(date, bag, sample)))+
facet_wrap(~temperature)+
scale_colour_gradientn(colours=c("blue", "lightblue", "white","pink", "red"))+
geom_point()+
geom_line()+
theme_classic()
In general there are higher rates for larger sizes.
Model using the final time point to quantify size effects on total fluorescence change.
final<-data%>%
filter(time=="4")model.size2<-lmer(sqrt(value) ~ temperature * scale(volume.mm3) + (1|bag), data=data)
summary(model.size2)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(value) ~ temperature * scale(volume.mm3) + (1 | bag)
## Data: data
##
## REML criterion at convergence: 5094.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.9936 -0.6613 -0.0292 0.7316 3.1762
##
## Random effects:
## Groups Name Variance Std.Dev.
## bag (Intercept) 0.01957 0.1399
## Residual 0.58951 0.7678
## Number of obs: 2190, groups: bag, 10
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 1.166e+00 5.061e-02 1.165e+01 23.042
## temperature42C -1.609e-01 3.408e-02 2.180e+03 -4.721
## scale(volume.mm3) 1.065e-01 2.773e-02 2.178e+03 3.842
## temperature42C:scale(volume.mm3) 1.619e-03 3.490e-02 2.183e+03 0.046
## Pr(>|t|)
## (Intercept) 4.40e-11 ***
## temperature42C 2.49e-06 ***
## scale(volume.mm3) 0.000125 ***
## temperature42C:scale(volume.mm3) 0.962998
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tmp42C sc(.3)
## tempertr42C -0.345
## scl(vlm.m3) 0.146 -0.212
## tmp42C:(.3) -0.108 0.057 -0.769anova(model.size2)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## temperature 13.1405 13.1405 1 2180.1 22.2904 2.493e-06
## scale(volume.mm3) 20.6361 20.6361 1 2149.5 35.0053 3.816e-09
## temperature:scale(volume.mm3) 0.0013 0.0013 1 2183.1 0.0022 0.963
##
## temperature ***
## scale(volume.mm3) ***
## temperature:scale(volume.mm3)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1rand(model.size2)## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## sqrt(value) ~ temperature + scale(volume.mm3) + (1 | bag) + temperature:scale(volume.mm3)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 6 -2547.4 5106.9
## (1 | bag) 5 -2568.2 5146.3 41.437 1 1.217e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1qqPlot(residuals(model.size2))
## [1] 1050 1030plot(Effect(c("volume.mm3"), model.size2))
Temperature and size affect metabolic rate.
Plot metabolic rates (y) over size range (x).
final%>%
ggplot(aes(x=volume.mm3, y=sqrt(value)))+
#facet_wrap(~temperature)+
geom_point()+
geom_smooth(method="lm")+
theme_classic()
There is a positive relationship between metabolic rate and size, but it is not particularly strong.
Plot correlation plot.
18°C
correlation18C <- lm(sqrt(value) ~ volume.mm3, data = final%>%filter(temperature=="18C"))
corrplot18C<-ggplot(final%>%filter(temperature=="18C"), aes(x = volume.mm3, y = sqrt(value))) +
geom_point() +
geom_smooth(method = "lm", se = TRUE) +
theme_classic()+
labs(title = "y=8.101e-06 + 1.631 (18°C)");corrplot18C
correlation42C <- lm(sqrt(value) ~ volume.mm3, data = final%>%filter(temperature=="42C"))
corrplot42C<-ggplot(final%>%filter(temperature=="42C"), aes(x = volume.mm3, y = sqrt(value))) +
geom_point() +
geom_smooth(method = "lm", se = TRUE) +
theme_classic()+
labs(title = "y=5.773e-06 + 1.233 (42°C)");corrplot42C
Size is important to consider, so we will normalize metabolic rates to size using value.mm3 generated above.
Model effects of time, hardening, and temperature
Detect outliers
Build a model including all predictors.
model<-lmer(value.mm3 ~ time * temperature * hardening + (1|bag) + (1|date:bag:sample), data=data)
qqPlot(residuals(model))
## [1] 1050 1046hist(data$value.mm3)
Identify using standardized residuals.
# Extract raw residuals
data$raw_resid <- residuals(model)
# Standardize residuals
data$std_resid <- data$raw_resid / sd(data$raw_resid)
# Flag potential outliers
outlier_threshold <- 3
data$outlier_flag <- abs(data$std_resid) > outlier_threshold
# Filter rows flagged as outliers
outliers <- data %>% filter(outlier_flag == TRUE)
print(outliers)## # A tibble: 34 × 16
## # Groups: date, bag, sample, width.mm, length.mm [29]
## date bag sample hardening temperature time status width.mm length.mm
## <dbl> <dbl> <chr> <chr> <chr> <fct> <dbl> <dbl> <dbl>
## 1 20240725 66 7 fresh-water 18C 4 0 15.9 24.3
## 2 20240729 37 2 control 18C 4 0 15.4 22.4
## 3 20240731 30 5 temperature 18C 4 0 15.5 22.5
## 4 20240801 75 13 fresh-wate… 18C 4 0 17.7 21.4
## 5 20240801 75 2 fresh-wate… 18C 4 0 16.3 21.7
## 6 20240801 75 20 fresh-wate… 18C 4 0 16.7 24.6
## 7 20240801 75 3 fresh-wate… 18C 4 0 17.7 22.7
## 8 20240801 75 5 fresh-wate… 18C 4 0 16.8 23.9
## 9 20240805 50 1 immune 18C 4 0 16.8 21.3
## 10 20240805 50 12 immune 18C 4 0 18.2 30.2
## # ℹ 24 more rows
## # ℹ 7 more variables: final.mortality <chr>, value <dbl>, volume.mm3 <dbl>,
## # value.mm3 <dbl>, raw_resid <dbl>, std_resid <dbl>, outlier_flag <lgl># Plot standardized residuals
ggplot(data, aes(x = seq_along(std_resid), y = std_resid)) +
geom_point(aes(color = outlier_flag), size = 2) +
geom_hline(yintercept = c(-outlier_threshold, outlier_threshold), linetype = "dashed", color = "red") +
labs(title = "Standardized Residuals with Outliers", x = "Index", y = "Standardized Residual") +
theme_minimal()
Remove identified outliers.
data<-data%>%
filter(!outlier_flag==TRUE)hist(data$value.mm3)
Manually remove outlier of 1 high observation in temperature hardened oysters (alive) at 42°C at the final time point.
data<-data%>%
filter(!c(time=="4"& hardening=="temperature" & final.mortality=="alive" & temperature=="42C" & value.mm3>0.0001))Analyze model
Plot raw data.
data%>%
ggplot(aes(x=time, y=value.mm3, colour=temperature, group=sample))+
facet_wrap(~bag*date*hardening)+
geom_point()+
geom_line()+
theme_classic()
model<-lmer(sqrt(value.mm3) ~ time * temperature * hardening + (1|hardening:bag) + (1|date:bag:sample), data=data)
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## sqrt(value.mm3) ~ time * temperature * hardening + (1 | hardening:bag) +
## (1 | date:bag:sample)
## Data: data
##
## REML criterion at convergence: -21281.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.02057 -0.52313 0.01036 0.53184 2.90672
##
## Random effects:
## Groups Name Variance Std.Dev.
## date:bag:sample (Intercept) 2.323e-06 0.0015241
## hardening:bag (Intercept) 4.047e-07 0.0006362
## Residual 1.379e-06 0.0011744
## Number of obs: 2155, groups: date:bag:sample, 438; hardening:bag, 10
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) 3.853e-05 5.176e-04
## time1 3.164e-03 2.162e-04
## time2 5.275e-03 2.162e-04
## time3 7.115e-03 2.162e-04
## time4 8.420e-03 2.185e-04
## temperature42C -2.446e-06 3.528e-04
## hardeningfresh-water -3.853e-05 7.502e-04
## hardeningfresh-water-temperature -3.853e-05 7.502e-04
## hardeningimmune 1.022e-04 7.512e-04
## hardeningtemperature 1.892e-05 7.510e-04
## time1:temperature42C 8.691e-04 3.045e-04
## time2:temperature42C -1.411e-04 3.045e-04
## time3:temperature42C -1.069e-03 3.045e-04
## time4:temperature42C -1.721e-03 3.061e-04
## time1:hardeningfresh-water 3.787e-04 3.402e-04
## time2:hardeningfresh-water 8.970e-04 3.402e-04
## time3:hardeningfresh-water 1.068e-03 3.402e-04
## time4:hardeningfresh-water 1.312e-03 3.466e-04
## time1:hardeningfresh-water-temperature 1.406e-04 3.402e-04
## time2:hardeningfresh-water-temperature 5.346e-04 3.402e-04
## time3:hardeningfresh-water-temperature 5.787e-04 3.402e-04
## time4:hardeningfresh-water-temperature 5.957e-04 3.503e-04
## time1:hardeningimmune 1.210e-03 3.428e-04
## time2:hardeningimmune 2.260e-03 3.423e-04
## time3:hardeningimmune 2.427e-03 3.428e-04
## time4:hardeningimmune 3.417e-03 3.742e-04
## time1:hardeningtemperature 4.978e-04 3.420e-04
## time2:hardeningtemperature 1.231e-03 3.420e-04
## time3:hardeningtemperature 1.334e-03 3.428e-04
## time4:hardeningtemperature 2.024e-03 3.513e-04
## temperature42C:hardeningfresh-water -4.293e-06 5.585e-04
## temperature42C:hardeningfresh-water-temperature 2.446e-06 5.564e-04
## temperature42C:hardeningimmune -1.383e-04 5.577e-04
## temperature42C:hardeningtemperature -5.500e-05 5.575e-04
## time1:temperature42C:hardeningfresh-water -2.605e-04 4.821e-04
## time2:temperature42C:hardeningfresh-water -6.516e-04 4.821e-04
## time3:temperature42C:hardeningfresh-water -9.117e-04 4.821e-04
## time4:temperature42C:hardeningfresh-water -1.103e-03 4.866e-04
## time1:temperature42C:hardeningfresh-water-temperature -1.267e-03 4.803e-04
## time2:temperature42C:hardeningfresh-water-temperature -1.480e-03 4.803e-04
## time3:temperature42C:hardeningfresh-water-temperature -1.567e-03 4.803e-04
## time4:temperature42C:hardeningfresh-water-temperature -1.497e-03 4.875e-04
## time1:temperature42C:hardeningimmune -4.731e-04 4.821e-04
## time2:temperature42C:hardeningimmune -1.527e-03 4.818e-04
## time3:temperature42C:hardeningimmune -1.855e-03 4.821e-04
## time4:temperature42C:hardeningimmune -2.981e-03 5.049e-04
## time1:temperature42C:hardeningtemperature 2.172e-05 4.815e-04
## time2:temperature42C:hardeningtemperature -3.477e-04 4.815e-04
## time3:temperature42C:hardeningtemperature -4.476e-04 4.821e-04
## time4:temperature42C:hardeningtemperature -1.049e-03 4.893e-04
## df t value
## (Intercept) 6.485e+00 0.074
## time1 1.666e+03 14.635
## time2 1.666e+03 24.397
## time3 1.666e+03 32.907
## time4 1.668e+03 38.534
## temperature42C 8.021e+02 -0.007
## hardeningfresh-water 7.165e+00 -0.051
## hardeningfresh-water-temperature 7.165e+00 -0.051
## hardeningimmune 7.202e+00 0.136
## hardeningtemperature 7.196e+00 0.025
## time1:temperature42C 1.666e+03 2.854
## time2:temperature42C 1.666e+03 -0.463
## time3:temperature42C 1.666e+03 -3.512
## time4:temperature42C 1.667e+03 -5.621
## time1:hardeningfresh-water 1.666e+03 1.113
## time2:hardeningfresh-water 1.666e+03 2.637
## time3:hardeningfresh-water 1.666e+03 3.140
## time4:hardeningfresh-water 1.670e+03 3.785
## time1:hardeningfresh-water-temperature 1.666e+03 0.413
## time2:hardeningfresh-water-temperature 1.666e+03 1.571
## time3:hardeningfresh-water-temperature 1.666e+03 1.701
## time4:hardeningfresh-water-temperature 1.671e+03 1.700
## time1:hardeningimmune 1.666e+03 3.530
## time2:hardeningimmune 1.673e+03 6.604
## time3:hardeningimmune 1.666e+03 7.081
## time4:hardeningimmune 1.681e+03 9.131
## time1:hardeningtemperature 1.669e+03 1.456
## time2:hardeningtemperature 1.669e+03 3.600
## time3:hardeningtemperature 1.666e+03 3.893
## time4:hardeningtemperature 1.671e+03 5.763
## temperature42C:hardeningfresh-water 8.021e+02 -0.008
## temperature42C:hardeningfresh-water-temperature 8.021e+02 0.004
## temperature42C:hardeningimmune 8.071e+02 -0.248
## temperature42C:hardeningtemperature 8.070e+02 -0.099
## time1:temperature42C:hardeningfresh-water 1.666e+03 -0.540
## time2:temperature42C:hardeningfresh-water 1.666e+03 -1.352
## time3:temperature42C:hardeningfresh-water 1.666e+03 -1.891
## time4:temperature42C:hardeningfresh-water 1.668e+03 -2.267
## time1:temperature42C:hardeningfresh-water-temperature 1.666e+03 -2.638
## time2:temperature42C:hardeningfresh-water-temperature 1.666e+03 -3.081
## time3:temperature42C:hardeningfresh-water-temperature 1.666e+03 -3.262
## time4:temperature42C:hardeningfresh-water-temperature 1.669e+03 -3.072
## time1:temperature42C:hardeningimmune 1.666e+03 -0.981
## time2:temperature42C:hardeningimmune 1.670e+03 -3.169
## time3:temperature42C:hardeningimmune 1.666e+03 -3.847
## time4:temperature42C:hardeningimmune 1.674e+03 -5.903
## time1:temperature42C:hardeningtemperature 1.668e+03 0.045
## time2:temperature42C:hardeningtemperature 1.668e+03 -0.722
## time3:temperature42C:hardeningtemperature 1.666e+03 -0.928
## time4:temperature42C:hardeningtemperature 1.669e+03 -2.144
## Pr(>|t|)
## (Intercept) 0.942910
## time1 < 2e-16 ***
## time2 < 2e-16 ***
## time3 < 2e-16 ***
## time4 < 2e-16 ***
## temperature42C 0.994470
## hardeningfresh-water 0.960447
## hardeningfresh-water-temperature 0.960447
## hardeningimmune 0.895516
## hardeningtemperature 0.980589
## time1:temperature42C 0.004368 **
## time2:temperature42C 0.643205
## time3:temperature42C 0.000457 ***
## time4:temperature42C 2.22e-08 ***
## time1:hardeningfresh-water 0.265766
## time2:hardeningfresh-water 0.008441 **
## time3:hardeningfresh-water 0.001716 **
## time4:hardeningfresh-water 0.000159 ***
## time1:hardeningfresh-water-temperature 0.679502
## time2:hardeningfresh-water-temperature 0.116261
## time3:hardeningfresh-water-temperature 0.089089 .
## time4:hardeningfresh-water-temperature 0.089226 .
## time1:hardeningimmune 0.000426 ***
## time2:hardeningimmune 5.35e-11 ***
## time3:hardeningimmune 2.10e-12 ***
## time4:hardeningimmune < 2e-16 ***
## time1:hardeningtemperature 0.145696
## time2:hardeningtemperature 0.000327 ***
## time3:hardeningtemperature 0.000103 ***
## time4:hardeningtemperature 9.83e-09 ***
## temperature42C:hardeningfresh-water 0.993869
## temperature42C:hardeningfresh-water-temperature 0.996493
## temperature42C:hardeningimmune 0.804249
## temperature42C:hardeningtemperature 0.921440
## time1:temperature42C:hardeningfresh-water 0.589017
## time2:temperature42C:hardeningfresh-water 0.176681
## time3:temperature42C:hardeningfresh-water 0.058789 .
## time4:temperature42C:hardeningfresh-water 0.023530 *
## time1:temperature42C:hardeningfresh-water-temperature 0.008412 **
## time2:temperature42C:hardeningfresh-water-temperature 0.002098 **
## time3:temperature42C:hardeningfresh-water-temperature 0.001128 **
## time4:temperature42C:hardeningfresh-water-temperature 0.002163 **
## time1:temperature42C:hardeningimmune 0.326529
## time2:temperature42C:hardeningimmune 0.001557 **
## time3:temperature42C:hardeningimmune 0.000124 ***
## time4:temperature42C:hardeningimmune 4.31e-09 ***
## time1:temperature42C:hardeningtemperature 0.964031
## time2:temperature42C:hardeningtemperature 0.470400
## time3:temperature42C:hardeningtemperature 0.353284
## time4:temperature42C:hardeningtemperature 0.032160 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value
## time 0.0177775 0.0044444 4 1669.06 3222.3687
## temperature 0.0000746 0.0000746 1 413.27 54.0834
## hardening 0.0000083 0.0000021 4 4.93 1.5128
## time:temperature 0.0008448 0.0002112 4 1669.07 153.1290
## time:hardening 0.0001694 0.0000106 16 1668.88 7.6747
## temperature:hardening 0.0000177 0.0000044 4 413.16 3.2056
## time:temperature:hardening 0.0000751 0.0000047 16 1668.88 3.4047
## Pr(>F)
## time < 2.2e-16 ***
## temperature 1.041e-12 ***
## hardening 0.32752
## time:temperature < 2.2e-16 ***
## time:hardening < 2.2e-16 ***
## temperature:hardening 0.01308 *
## time:temperature:hardening 5.528e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1rand(model)## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## sqrt(value.mm3) ~ time + temperature + hardening + (1 | hardening:bag) + (1 | date:bag:sample) + time:temperature + time:hardening + temperature:hardening + time:temperature:hardening
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 53 10641 -21175
## (1 | hardening:bag) 52 10630 -21157 20.16 1 7.123e-06 ***
## (1 | date:bag:sample) 52 10110 -20116 1061.65 1 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1qqPlot(residuals(model))
## [1] 1775 529Significant effects of time x temperature x hardening, indicating different slopes in metabolic rate between temperatures modulated by hardening treatment.
Plot data
Plot mean response for each hardening treatment across time at 18°C and 42°C.
Plot first with individual points with geom smooth lines.
plot1<-data%>%
ggplot(aes(x=time, y=value.mm3, color=temperature, fill=temperature))+
facet_grid(~hardening)+
geom_point(alpha=0.5)+
geom_smooth(aes(group=temperature))+
scale_colour_manual(values=c("cyan4", "orange"))+
scale_fill_manual(values=c("cyan4", "orange"))+
theme_classic()+
xlab("Hour");plot1
plot1a<-data%>%
ggplot(aes(x=time, y=value.mm3, color=hardening, fill=hardening))+
facet_grid(~temperature)+
geom_point(alpha=0.5)+
geom_smooth(aes(group=hardening))+
#scale_colour_manual(values=c("cyan4", "orange"))+
#scale_fill_manual(values=c("cyan4", "orange"))+
theme_classic()+
xlab("Hour");plot1a
Next plot with mean and sem for each group.
plot2<-data%>%
group_by(temperature, hardening, time)%>%
summarize(mean=mean(value.mm3, na.rm=TRUE), se=sd(value.mm3, na.rm=TRUE)/sqrt(length(value.mm3)))%>%
ggplot(aes(x=time, y=mean, color=temperature, fill=temperature))+
facet_grid(~hardening)+
geom_point(alpha=0.5)+
geom_errorbar(aes(ymin=mean-se, ymax=mean+se), width=0.1)+
geom_line(aes(group=temperature))+
scale_colour_manual(values=c("cyan4", "orange"))+
scale_fill_manual(values=c("cyan4", "orange"))+
theme_classic()+
xlab("Hour");plot2
plot2a<-data%>%
group_by(temperature, hardening, time)%>%
summarise(mean=mean(value.mm3, na.rm=TRUE), se=sd(value.mm3, na.rm=TRUE)/sqrt(length(value.mm3)))%>%
ggplot(aes(x=time, y=mean, color=hardening, fill=hardening))+
facet_grid(~temperature)+
geom_errorbar(aes(ymin=mean-se, ymax=mean+se), width=0.1)+
geom_point(alpha=0.5)+
geom_line(aes(group=hardening))+
#scale_colour_manual(values=c("cyan4", "orange"))+
#scale_fill_manual(values=c("cyan4", "orange"))+
theme_classic()+
xlab("Hour");plot2a
Conduct post hoc tests
Effects of hardening treatment within temperature
anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value
## time 0.0177775 0.0044444 4 1669.06 3222.3687
## temperature 0.0000746 0.0000746 1 413.27 54.0834
## hardening 0.0000083 0.0000021 4 4.93 1.5128
## time:temperature 0.0008448 0.0002112 4 1669.07 153.1290
## time:hardening 0.0001694 0.0000106 16 1668.88 7.6747
## temperature:hardening 0.0000177 0.0000044 4 413.16 3.2056
## time:temperature:hardening 0.0000751 0.0000047 16 1668.88 3.4047
## Pr(>F)
## time < 2.2e-16 ***
## temperature 1.041e-12 ***
## hardening 0.32752
## time:temperature < 2.2e-16 ***
## time:hardening < 2.2e-16 ***
## temperature:hardening 0.01308 *
## time:temperature:hardening 5.528e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1emm<-emmeans(model, ~hardening|temperature|time, adjust = "tukey")
pairs(emm)## temperature = 18C, time = 0:
## contrast estimate SE df t.ratio
## control - (fresh-water) 3.85e-05 0.000750 7.26 0.051
## control - (fresh-water-temperature) 3.85e-05 0.000750 7.26 0.051
## control - immune -1.02e-04 0.000751 7.29 -0.136
## control - temperature -1.89e-05 0.000751 7.29 -0.025
## (fresh-water) - (fresh-water-temperature) 0.00e+00 0.000768 7.98 0.000
## (fresh-water) - immune -1.41e-04 0.000769 8.02 -0.183
## (fresh-water) - temperature -5.74e-05 0.000769 8.01 -0.075
## (fresh-water-temperature) - immune -1.41e-04 0.000769 8.02 -0.183
## (fresh-water-temperature) - temperature -5.74e-05 0.000769 8.01 -0.075
## immune - temperature 8.33e-05 0.000770 8.05 0.108
## p.value
## 1.0000
## 1.0000
## 0.9999
## 1.0000
## 1.0000
## 0.9997
## 1.0000
## 0.9997
## 1.0000
## 1.0000
##
## temperature = 42C, time = 0:
## contrast estimate SE df t.ratio
## control - (fresh-water) 4.28e-05 0.000751 7.28 0.057
## control - (fresh-water-temperature) 3.61e-05 0.000749 7.22 0.048
## control - immune 3.61e-05 0.000749 7.22 0.048
## control - temperature 3.61e-05 0.000749 7.22 0.048
## (fresh-water) - (fresh-water-temperature) -6.74e-06 0.000770 8.04 -0.009
## (fresh-water) - immune -6.74e-06 0.000770 8.04 -0.009
## (fresh-water) - temperature -6.74e-06 0.000770 8.04 -0.009
## (fresh-water-temperature) - immune 0.00e+00 0.000768 7.98 0.000
## (fresh-water-temperature) - temperature 0.00e+00 0.000768 7.98 0.000
## immune - temperature 0.00e+00 0.000768 7.98 0.000
## p.value
## 1.0000
## 1.0000
## 1.0000
## 1.0000
## 1.0000
## 1.0000
## 1.0000
## 1.0000
## 1.0000
## 1.0000
##
## temperature = 18C, time = 1:
## contrast estimate SE df t.ratio
## control - (fresh-water) -3.40e-04 0.000750 7.26 -0.453
## control - (fresh-water-temperature) -1.02e-04 0.000750 7.26 -0.136
## control - immune -1.31e-03 0.000751 7.29 -1.747
## control - temperature -5.17e-04 0.000750 7.26 -0.689
## (fresh-water) - (fresh-water-temperature) 2.38e-04 0.000768 7.98 0.310
## (fresh-water) - immune -9.72e-04 0.000769 8.02 -1.264
## (fresh-water) - temperature -1.77e-04 0.000768 7.98 -0.230
## (fresh-water-temperature) - immune -1.21e-03 0.000769 8.02 -1.574
## (fresh-water-temperature) - temperature -4.15e-04 0.000768 7.98 -0.540
## immune - temperature 7.96e-04 0.000769 8.02 1.035
## p.value
## 0.9894
## 0.9999
## 0.4645
## 0.9530
## 0.9975
## 0.7181
## 0.9992
## 0.5494
## 0.9802
## 0.8331
##
## temperature = 42C, time = 1:
## contrast estimate SE df t.ratio
## control - (fresh-water) -7.54e-05 0.000751 7.28 -0.100
## control - (fresh-water-temperature) 1.16e-03 0.000749 7.22 1.551
## control - immune -7.01e-04 0.000749 7.22 -0.935
## control - temperature -4.83e-04 0.000749 7.22 -0.645
## (fresh-water) - (fresh-water-temperature) 1.24e-03 0.000770 8.04 1.609
## (fresh-water) - immune -6.25e-04 0.000770 8.04 -0.813
## (fresh-water) - temperature -4.08e-04 0.000770 8.04 -0.530
## (fresh-water-temperature) - immune -1.86e-03 0.000768 7.98 -2.426
## (fresh-water-temperature) - temperature -1.65e-03 0.000768 7.98 -2.143
## immune - temperature 2.17e-04 0.000768 7.98 0.283
## p.value
## 1.0000
## 0.5646
## 0.8749
## 0.9624
## 0.5308
## 0.9195
## 0.9815
## 0.2019
## 0.2900
## 0.9983
##
## temperature = 18C, time = 2:
## contrast estimate SE df t.ratio
## control - (fresh-water) -8.59e-04 0.000750 7.26 -1.144
## control - (fresh-water-temperature) -4.96e-04 0.000750 7.26 -0.661
## control - immune -2.36e-03 0.000750 7.26 -3.149
## control - temperature -1.25e-03 0.000750 7.26 -1.666
## (fresh-water) - (fresh-water-temperature) 3.62e-04 0.000768 7.98 0.472
## (fresh-water) - immune -1.50e-03 0.000768 7.98 -1.959
## (fresh-water) - temperature -3.92e-04 0.000768 7.98 -0.510
## (fresh-water-temperature) - immune -1.87e-03 0.000768 7.98 -2.431
## (fresh-water-temperature) - temperature -7.54e-04 0.000768 7.98 -0.982
## immune - temperature 1.11e-03 0.000768 7.98 1.449
## p.value
## 0.7806
## 0.9591
## 0.0830
## 0.5048
## 0.9879
## 0.3625
## 0.9839
## 0.2008
## 0.8563
## 0.6176
##
## temperature = 42C, time = 2:
## contrast estimate SE df t.ratio
## control - (fresh-water) -2.03e-04 0.000751 7.28 -0.270
## control - (fresh-water-temperature) 9.81e-04 0.000749 7.22 1.309
## control - immune -6.98e-04 0.000749 7.22 -0.931
## control - temperature -8.47e-04 0.000749 7.22 -1.131
## (fresh-water) - (fresh-water-temperature) 1.18e-03 0.000770 8.04 1.538
## (fresh-water) - immune -4.95e-04 0.000770 8.04 -0.643
## (fresh-water) - temperature -6.45e-04 0.000770 8.04 -0.838
## (fresh-water-temperature) - immune -1.68e-03 0.000768 7.98 -2.186
## (fresh-water-temperature) - temperature -1.83e-03 0.000768 7.98 -2.381
## immune - temperature -1.50e-04 0.000768 7.98 -0.195
## p.value
## 0.9985
## 0.6948
## 0.8766
## 0.7871
## 0.5685
## 0.9632
## 0.9113
## 0.2749
## 0.2142
## 0.9996
##
## temperature = 18C, time = 3:
## contrast estimate SE df t.ratio
## control - (fresh-water) -1.03e-03 0.000750 7.26 -1.372
## control - (fresh-water-temperature) -5.40e-04 0.000750 7.26 -0.720
## control - immune -2.53e-03 0.000751 7.29 -3.366
## control - temperature -1.35e-03 0.000751 7.29 -1.801
## (fresh-water) - (fresh-water-temperature) 4.90e-04 0.000768 7.98 0.637
## (fresh-water) - immune -1.50e-03 0.000769 8.02 -1.950
## (fresh-water) - temperature -3.23e-04 0.000769 8.01 -0.421
## (fresh-water-temperature) - immune -1.99e-03 0.000769 8.02 -2.587
## (fresh-water-temperature) - temperature -8.13e-04 0.000769 8.01 -1.058
## immune - temperature 1.18e-03 0.000770 8.05 1.528
## p.value
## 0.6608
## 0.9454
## 0.0623
## 0.4383
## 0.9643
## 0.3658
## 0.9921
## 0.1629
## 0.8226
## 0.5740
##
## temperature = 42C, time = 3:
## contrast estimate SE df t.ratio
## control - (fresh-water) -1.14e-04 0.000751 7.28 -0.152
## control - (fresh-water-temperature) 1.02e-03 0.000749 7.22 1.366
## control - immune -5.36e-04 0.000749 7.22 -0.716
## control - temperature -8.51e-04 0.000749 7.22 -1.135
## (fresh-water) - (fresh-water-temperature) 1.14e-03 0.000770 8.04 1.479
## (fresh-water) - immune -4.22e-04 0.000770 8.04 -0.549
## (fresh-water) - temperature -7.37e-04 0.000770 8.04 -0.957
## (fresh-water-temperature) - immune -1.56e-03 0.000768 7.98 -2.032
## (fresh-water-temperature) - temperature -1.87e-03 0.000768 7.98 -2.441
## immune - temperature -3.14e-04 0.000768 7.98 -0.409
## p.value
## 0.9999
## 0.6640
## 0.9465
## 0.7851
## 0.6010
## 0.9790
## 0.8666
## 0.3323
## 0.1981
## 0.9929
##
## temperature = 18C, time = 4:
## contrast estimate SE df t.ratio
## control - (fresh-water) -1.27e-03 0.000753 7.37 -1.690
## control - (fresh-water-temperature) -5.57e-04 0.000755 7.44 -0.738
## control - immune -3.52e-03 0.000766 7.89 -4.592
## control - temperature -2.04e-03 0.000755 7.44 -2.706
## (fresh-water) - (fresh-water-temperature) 7.16e-04 0.000774 8.24 0.925
## (fresh-water) - immune -2.25e-03 0.000785 8.71 -2.861
## (fresh-water) - temperature -7.70e-04 0.000774 8.24 -0.995
## (fresh-water-temperature) - immune -2.96e-03 0.000787 8.78 -3.765
## (fresh-water-temperature) - temperature -1.49e-03 0.000776 8.31 -1.915
## immune - temperature 1.48e-03 0.000787 8.79 1.875
## p.value
## 0.4920
## 0.9409
## 0.0116
## 0.1449
## 0.8798
## 0.1063
## 0.8510
## 0.0288
## 0.3788
## 0.3939
##
## temperature = 42C, time = 4:
## contrast estimate SE df t.ratio
## control - (fresh-water) -1.66e-04 0.000751 7.28 -0.221
## control - (fresh-water-temperature) 9.38e-04 0.000749 7.22 1.251
## control - immune -4.00e-04 0.000749 7.22 -0.534
## control - temperature -9.39e-04 0.000750 7.25 -1.252
## (fresh-water) - (fresh-water-temperature) 1.10e-03 0.000770 8.04 1.434
## (fresh-water) - immune -2.34e-04 0.000770 8.04 -0.304
## (fresh-water) - temperature -7.73e-04 0.000770 8.07 -1.004
## (fresh-water-temperature) - immune -1.34e-03 0.000768 7.98 -1.742
## (fresh-water-temperature) - temperature -1.88e-03 0.000769 8.01 -2.442
## immune - temperature -5.39e-04 0.000769 8.01 -0.702
## p.value
## 0.9993
## 0.7255
## 0.9808
## 0.7252
## 0.6254
## 0.9977
## 0.8468
## 0.4627
## 0.1976
## 0.9504
##
## Note: contrasts are still on the sqrt scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimatesSignificant effects:
- Time 4 at 18°C: Immune higher than control and fresh-water-temperature.
No differences at 42°C are significant.
Effects of temperature treatment within hardening
emm<-emmeans(model, ~temperature|hardening|time, adjust = "tukey")
pairs(emm)## hardening = control, time = 0:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 2.45e-06 0.000353 817 0.007 0.9945
##
## hardening = fresh-water, time = 0:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 6.74e-06 0.000433 817 0.016 0.9876
##
## hardening = fresh-water-temperature, time = 0:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 0.00e+00 0.000430 818 0.000 1.0000
##
## hardening = immune, time = 0:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 1.41e-04 0.000432 826 0.326 0.7447
##
## hardening = temperature, time = 0:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 5.74e-05 0.000432 826 0.133 0.8942
##
## hardening = control, time = 1:
## contrast estimate SE df t.ratio p.value
## 18C - 42C -8.67e-04 0.000353 817 -2.457 0.0142
##
## hardening = fresh-water, time = 1:
## contrast estimate SE df t.ratio p.value
## 18C - 42C -6.02e-04 0.000433 817 -1.390 0.1649
##
## hardening = fresh-water-temperature, time = 1:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 3.98e-04 0.000430 818 0.925 0.3553
##
## hardening = immune, time = 1:
## contrast estimate SE df t.ratio p.value
## 18C - 42C -2.55e-04 0.000432 826 -0.591 0.5547
##
## hardening = temperature, time = 1:
## contrast estimate SE df t.ratio p.value
## 18C - 42C -8.33e-04 0.000430 818 -1.937 0.0531
##
## hardening = control, time = 2:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 1.44e-04 0.000353 817 0.407 0.6842
##
## hardening = fresh-water, time = 2:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 7.99e-04 0.000433 817 1.846 0.0652
##
## hardening = fresh-water-temperature, time = 2:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 1.62e-03 0.000430 818 3.767 0.0002
##
## hardening = immune, time = 2:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 1.81e-03 0.000430 818 4.204 <.0001
##
## hardening = temperature, time = 2:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 5.46e-04 0.000430 818 1.270 0.2046
##
## hardening = control, time = 3:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 1.07e-03 0.000353 817 3.038 0.0025
##
## hardening = fresh-water, time = 3:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 1.99e-03 0.000433 817 4.590 <.0001
##
## hardening = fresh-water-temperature, time = 3:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 2.64e-03 0.000430 818 6.127 <.0001
##
## hardening = immune, time = 3:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 3.06e-03 0.000432 826 7.096 <.0001
##
## hardening = temperature, time = 3:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 1.57e-03 0.000432 826 3.647 0.0003
##
## hardening = control, time = 4:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 1.72e-03 0.000354 828 4.865 <.0001
##
## hardening = fresh-water, time = 4:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 2.83e-03 0.000437 842 6.479 <.0001
##
## hardening = fresh-water-temperature, time = 4:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 3.22e-03 0.000437 861 7.362 <.0001
##
## hardening = immune, time = 4:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 4.84e-03 0.000456 981 10.615 <.0001
##
## hardening = temperature, time = 4:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 2.83e-03 0.000439 869 6.447 <.0001
##
## Note: contrasts are still on the sqrt scale
## Degrees-of-freedom method: kenward-rogerSignificant effects:
- Time 1: Control lower at 18°C
- Time 2: Fresh-water-temperature and immune lower at 42°C
- Time 3: All groups lower at 42°C
- Time 4: All groups lower at 42°C
Model at time final without mortality status
Detect outliers
Build a model including all predictors.
final<-data%>%
filter(time==4)
model2<-lmer(sqrt(value.mm3) ~ temperature * hardening + (1|hardening:bag), data=final)
summary(model2)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(value.mm3) ~ temperature * hardening + (1 | hardening:bag)
## Data: final
##
## REML criterion at convergence: -3627.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.38325 -0.72929 0.05586 0.74974 2.22629
##
## Random effects:
## Groups Name Variance Std.Dev.
## hardening:bag (Intercept) 8.629e-07 0.0009289
## Residual 5.737e-06 0.0023951
## Number of obs: 408, groups: hardening:bag, 10
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) 8.491e-03 7.340e-04
## temperature42C -1.680e-03 4.431e-04
## hardeningfresh-water 1.115e-03 1.061e-03
## hardeningfresh-water-temperature 3.488e-04 1.066e-03
## hardeningimmune 3.973e-03 1.092e-03
## hardeningtemperature 2.124e-03 1.065e-03
## temperature42C:hardeningfresh-water -1.032e-03 7.060e-04
## temperature42C:hardeningfresh-water-temperature -1.362e-03 7.106e-04
## temperature42C:hardeningimmune -3.648e-03 7.489e-04
## temperature42C:hardeningtemperature -1.319e-03 7.124e-04
## df t value Pr(>|t|)
## (Intercept) 5.604e+00 11.567 4.02e-05 ***
## temperature42C 3.930e+02 -3.792 0.000173 ***
## hardeningfresh-water 6.122e+00 1.051 0.332858
## hardeningfresh-water-temperature 6.229e+00 0.327 0.754114
## hardeningimmune 6.858e+00 3.640 0.008585 **
## hardeningtemperature 6.222e+00 1.994 0.091541 .
## temperature42C:hardeningfresh-water 3.930e+02 -1.462 0.144661
## temperature42C:hardeningfresh-water-temperature 3.933e+02 -1.916 0.056085 .
## temperature42C:hardeningimmune 3.931e+02 -4.872 1.61e-06 ***
## temperature42C:hardeningtemperature 3.930e+02 -1.852 0.064830 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tmp42C hrdnn- hrdn-- hrdnngm hrdnngt tm42C:- t42C:--
## tempertr42C -0.311
## hrdnngfrsh- -0.692 0.215
## hrdnngfrs-- -0.689 0.215 0.477
## hardenngmmn -0.673 0.209 0.465 0.463
## hrdnngtmprt -0.689 0.215 0.477 0.475 0.463
## tmprtr42C:- 0.195 -0.628 -0.342 -0.135 -0.131 -0.135
## tmprt42C:-- 0.194 -0.624 -0.134 -0.352 -0.131 -0.134 0.391
## tmprtr42C:hrdnngm 0.184 -0.592 -0.127 -0.127 -0.394 -0.127 0.371 0.369
## tmprtr42C:hrdnngt 0.194 -0.622 -0.134 -0.133 -0.130 -0.350 0.390 0.388
## tmprtr42C:hrdnngm
## tempertr42C
## hrdnngfrsh-
## hrdnngfrs--
## hardenngmmn
## hrdnngtmprt
## tmprtr42C:-
## tmprt42C:--
## tmprtr42C:hrdnngm
## tmprtr42C:hrdnngt 0.368qqPlot(residuals(model2))
## [1] 74 260hist(final$value.mm3)
Identify using standardized residuals.
# Extract raw residuals
final$raw_resid <- residuals(model2)
# Standardize residuals
final$std_resid <- final$raw_resid / sd(final$raw_resid)
# Flag potential outliers
outlier_threshold <- 3
final$outlier_flag <- abs(final$std_resid) > outlier_threshold
# Filter rows flagged as outliers
outliers <- final %>% filter(outlier_flag == TRUE)
print(outliers)## # A tibble: 0 × 16
## # Groups: date, bag, sample, width.mm, length.mm [0]
## # ℹ 16 variables: date <dbl>, bag <dbl>, sample <chr>, hardening <chr>,
## # temperature <chr>, time <fct>, status <dbl>, width.mm <dbl>,
## # length.mm <dbl>, final.mortality <chr>, value <dbl>, volume.mm3 <dbl>,
## # value.mm3 <dbl>, raw_resid <dbl>, std_resid <dbl>, outlier_flag <lgl># Plot standardized residuals
ggplot(final, aes(x = seq_along(std_resid), y = std_resid)) +
geom_point(aes(color = outlier_flag), size = 2) +
geom_hline(yintercept = c(-outlier_threshold, outlier_threshold), linetype = "dashed", color = "red") +
labs(title = "Standardized Residuals with Outliers", x = "Index", y = "Standardized Residual") +
theme_minimal()
No outliers detected.
hist(final$value.mm3)
Analyze model
Plot raw data.
final%>%
ggplot(aes(x=hardening, y=value.mm3, colour=temperature, group=sample))+
geom_point()+
theme_classic()
Analyze total change in fluorescence (fluorescence after 4 hours).
model2<-lmer(sqrt(value.mm3) ~ temperature * hardening + (1|hardening:bag), data=final)
summary(model2)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(value.mm3) ~ temperature * hardening + (1 | hardening:bag)
## Data: final
##
## REML criterion at convergence: -3627.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.38325 -0.72929 0.05586 0.74974 2.22629
##
## Random effects:
## Groups Name Variance Std.Dev.
## hardening:bag (Intercept) 8.629e-07 0.0009289
## Residual 5.737e-06 0.0023951
## Number of obs: 408, groups: hardening:bag, 10
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) 8.491e-03 7.340e-04
## temperature42C -1.680e-03 4.431e-04
## hardeningfresh-water 1.115e-03 1.061e-03
## hardeningfresh-water-temperature 3.488e-04 1.066e-03
## hardeningimmune 3.973e-03 1.092e-03
## hardeningtemperature 2.124e-03 1.065e-03
## temperature42C:hardeningfresh-water -1.032e-03 7.060e-04
## temperature42C:hardeningfresh-water-temperature -1.362e-03 7.106e-04
## temperature42C:hardeningimmune -3.648e-03 7.489e-04
## temperature42C:hardeningtemperature -1.319e-03 7.124e-04
## df t value Pr(>|t|)
## (Intercept) 5.604e+00 11.567 4.02e-05 ***
## temperature42C 3.930e+02 -3.792 0.000173 ***
## hardeningfresh-water 6.122e+00 1.051 0.332858
## hardeningfresh-water-temperature 6.229e+00 0.327 0.754114
## hardeningimmune 6.858e+00 3.640 0.008585 **
## hardeningtemperature 6.222e+00 1.994 0.091541 .
## temperature42C:hardeningfresh-water 3.930e+02 -1.462 0.144661
## temperature42C:hardeningfresh-water-temperature 3.933e+02 -1.916 0.056085 .
## temperature42C:hardeningimmune 3.931e+02 -4.872 1.61e-06 ***
## temperature42C:hardeningtemperature 3.930e+02 -1.852 0.064830 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tmp42C hrdnn- hrdn-- hrdnngm hrdnngt tm42C:- t42C:--
## tempertr42C -0.311
## hrdnngfrsh- -0.692 0.215
## hrdnngfrs-- -0.689 0.215 0.477
## hardenngmmn -0.673 0.209 0.465 0.463
## hrdnngtmprt -0.689 0.215 0.477 0.475 0.463
## tmprtr42C:- 0.195 -0.628 -0.342 -0.135 -0.131 -0.135
## tmprt42C:-- 0.194 -0.624 -0.134 -0.352 -0.131 -0.134 0.391
## tmprtr42C:hrdnngm 0.184 -0.592 -0.127 -0.127 -0.394 -0.127 0.371 0.369
## tmprtr42C:hrdnngt 0.194 -0.622 -0.134 -0.133 -0.130 -0.350 0.390 0.388
## tmprtr42C:hrdnngm
## tempertr42C
## hrdnngfrsh-
## hrdnngfrs--
## hardenngmmn
## hrdnngtmprt
## tmprtr42C:-
## tmprt42C:--
## tmprtr42C:hrdnngm
## tmprtr42C:hrdnngt 0.368anova(model2)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## temperature 0.00096099 0.00096099 1 393.16 167.5191 < 2.2e-16 ***
## hardening 0.00004731 0.00001183 4 4.96 2.0619 0.2245928
## temperature:hardening 0.00013739 0.00003435 4 393.15 5.9876 0.0001099 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1rand(model2)## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## sqrt(value.mm3) ~ temperature + hardening + (1 | hardening:bag) + temperature:hardening
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 12 1813.7 -3603.4
## (1 | hardening:bag) 11 1804.8 -3587.5 17.887 1 2.344e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1qqPlot(residuals(model2))
## [1] 74 260Plot data
Plot mean response for each hardening treatment at 18°C and 42°C.
Plot first with individual points.
plot3<-final%>%
ggplot(aes(x=hardening, y=value.mm3, color=temperature))+
geom_boxplot(position=position_dodge(0.5))+
geom_point(alpha=0.5, position=position_dodge(0.5))+
scale_colour_manual(values=c("cyan4", "orange"))+
theme_classic()+
xlab("Hardening Treatment");plot3
plot3a<-final%>%
ggplot(aes(x=temperature, y=value.mm3, color=hardening))+
geom_boxplot(position=position_dodge(0.9))+
geom_point(alpha=0.5, position=position_dodge(0.9))+
#scale_colour_manual(values=c("cyan4", "orange"))+
theme_classic()+
xlab("Temperature");plot3a
Next plot with mean and sem for each group.
plot4<-final%>%
group_by(temperature, hardening)%>%
summarise(mean=mean(value.mm3, na.rm=TRUE), se=sd(value.mm3, na.rm=TRUE)/sqrt(length(value.mm3)))%>%
ggplot(aes(x=hardening, y=mean, color=temperature, fill=temperature))+
geom_point(alpha=0.5)+
geom_errorbar(aes(ymin=mean-se, ymax=mean+se), width=0.1)+
scale_colour_manual(values=c("cyan4", "orange"))+
scale_fill_manual(values=c("cyan4", "orange"))+
theme_classic()+
xlab("Hardening Treatment");plot4
plot4a<-final%>%
group_by(temperature, hardening)%>%
summarise(mean=mean(value.mm3, na.rm=TRUE), se=sd(value.mm3, na.rm=TRUE)/sqrt(length(value.mm3)))%>%
ggplot(aes(x=temperature, y=mean, color=hardening, fill=hardening))+
geom_point(alpha=0.5, position=position_dodge(0.7))+
geom_errorbar(aes(ymin=mean-se, ymax=mean+se), width=0.1, position=position_dodge(0.7))+
#scale_colour_manual(values=c("cyan4", "orange"))+
#scale_fill_manual(values=c("cyan4", "orange"))+
theme_classic()+
xlab("Temperature");plot4a
Conduct posthoc tests
Effects of hardening treatment within temperature
anova(model2)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## temperature 0.00096099 0.00096099 1 393.16 167.5191 < 2.2e-16 ***
## hardening 0.00004731 0.00001183 4 4.96 2.0619 0.2245928
## temperature:hardening 0.00013739 0.00003435 4 393.15 5.9876 0.0001099 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1emm<-emmeans(model2, ~hardening|temperature, adjust = "tukey")
pairs(emm)## temperature = 18C:
## contrast estimate SE df t.ratio
## control - (fresh-water) -1.12e-03 0.00106 6.17 -1.051
## control - (fresh-water-temperature) -3.49e-04 0.00107 6.28 -0.327
## control - immune -3.97e-03 0.00109 6.92 -3.639
## control - temperature -2.12e-03 0.00107 6.28 -1.993
## (fresh-water) - (fresh-water-temperature) 7.66e-04 0.00109 6.83 0.704
## (fresh-water) - immune -2.86e-03 0.00111 7.49 -2.567
## (fresh-water) - temperature -1.01e-03 0.00109 6.83 -0.927
## (fresh-water-temperature) - immune -3.62e-03 0.00112 7.61 -3.242
## (fresh-water-temperature) - temperature -1.77e-03 0.00109 6.94 -1.625
## immune - temperature 1.85e-03 0.00112 7.60 1.655
## p.value
## 0.8245
## 0.9968
## 0.0471
## 0.3647
## 0.9489
## 0.1727
## 0.8776
## 0.0701
## 0.5275
## 0.5084
##
## temperature = 42C:
## contrast estimate SE df t.ratio
## control - (fresh-water) -8.33e-05 0.00105 6.02 -0.079
## control - (fresh-water-temperature) 1.01e-03 0.00105 5.98 0.962
## control - immune -3.25e-04 0.00105 5.98 -0.309
## control - temperature -8.04e-04 0.00105 6.02 -0.763
## (fresh-water) - (fresh-water-temperature) 1.10e-03 0.00107 6.50 1.021
## (fresh-water) - immune -2.42e-04 0.00107 6.50 -0.225
## (fresh-water) - temperature -7.21e-04 0.00108 6.54 -0.670
## (fresh-water-temperature) - immune -1.34e-03 0.00107 6.46 -1.248
## (fresh-water-temperature) - temperature -1.82e-03 0.00107 6.50 -1.692
## immune - temperature -4.79e-04 0.00107 6.50 -0.446
## p.value
## 1.0000
## 0.8628
## 0.9974
## 0.9326
## 0.8384
## 0.9993
## 0.9565
## 0.7281
## 0.4967
## 0.9898
##
## Note: contrasts are still on the sqrt scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 5 estimatesSignificant effects:
- 18°C: Immune higher than control
No differences at 42°C are significant.
Effects of temperature treatment within hardening
emm<-emmeans(model, ~temperature|hardening, adjust = "tukey")
pairs(emm)## hardening = control:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 0.000415 0.000296 421 1.403 0.1613
##
## hardening = fresh-water:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 0.001005 0.000363 422 2.768 0.0059
##
## hardening = fresh-water-temperature:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 0.001575 0.000361 422 4.364 <.0001
##
## hardening = immune:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 0.001920 0.000362 429 5.299 <.0001
##
## hardening = temperature:
## contrast estimate SE df t.ratio p.value
## 18C - 42C 0.000834 0.000361 424 2.311 0.0213
##
## Results are averaged over the levels of: time
## Note: contrasts are still on the sqrt scale
## Degrees-of-freedom method: kenward-rogerSignificant effects:
- Control is different between temperatures
- Fresh water, fresh water temperature, immune, and temperature hardening are all lower at 42°C
Model at time final with mortality status
Detect outliers
Build a model including all predictors.
final_mort<-data%>%
filter(time==4)
model3<-lmer(sqrt(value.mm3) ~ temperature * hardening * final.mortality + (1|hardening:bag), data=final_mort)
qqPlot(residuals(model3))
## [1] 74 121hist(final_mort$value.mm3)
Identify using standardized residuals.
# Extract raw residuals
final_mort$raw_resid <- residuals(model3)
# Standardize residuals
final_mort$std_resid <- final_mort$raw_resid / sd(final_mort$raw_resid)
# Flag potential outliers
outlier_threshold <- 3
final_mort$outlier_flag <- abs(final_mort$std_resid) > outlier_threshold
# Filter rows flagged as outliers
outliers <- final_mort %>% filter(outlier_flag == TRUE)
print(outliers)## # A tibble: 0 × 16
## # Groups: date, bag, sample, width.mm, length.mm [0]
## # ℹ 16 variables: date <dbl>, bag <dbl>, sample <chr>, hardening <chr>,
## # temperature <chr>, time <fct>, status <dbl>, width.mm <dbl>,
## # length.mm <dbl>, final.mortality <chr>, value <dbl>, volume.mm3 <dbl>,
## # value.mm3 <dbl>, raw_resid <dbl>, std_resid <dbl>, outlier_flag <lgl># Plot standardized residuals
ggplot(final_mort, aes(x = seq_along(std_resid), y = std_resid)) +
geom_point(aes(color = outlier_flag), size = 2) +
geom_hline(yintercept = c(-outlier_threshold, outlier_threshold), linetype = "dashed", color = "red") +
labs(title = "Standardized Residuals with Outliers", x = "Index", y = "Standardized Residual") +
theme_minimal()
No outliers detected, use the “final” data frame since no observations needed to be removed.
hist(final$value.mm3)
Analyze model
Plot raw data.
final%>%
ggplot(aes(x=hardening, y=value.mm3, colour=temperature, group=sample))+
facet_wrap(~final.mortality)+
geom_point(position=position_dodge(0.5))+
theme_classic()
Analyze total change in fluorescence (fluorescence after 4 hours) for each treatment and comparing those that ended up alive or dead at the end of the trial.
model3<-lmer(sqrt(value.mm3) ~ temperature * hardening * final.mortality + (1|hardening:bag), data=final)
summary(model3)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(value.mm3) ~ temperature * hardening * final.mortality +
## (1 | hardening:bag)
## Data: final
##
## REML criterion at convergence: -3540.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.45267 -0.64455 0.08197 0.63880 2.31938
##
## Random effects:
## Groups Name Variance Std.Dev.
## hardening:bag (Intercept) 7.792e-07 0.0008827
## Residual 5.387e-06 0.0023210
## Number of obs: 408, groups: hardening:bag, 10
##
## Fixed effects:
## Estimate
## (Intercept) 8.156e-03
## temperature42C -2.182e-03
## hardeningfresh-water 1.416e-03
## hardeningfresh-water-temperature 7.474e-04
## hardeningimmune 4.520e-03
## hardeningtemperature 2.564e-03
## final.mortalitydead 1.355e-03
## temperature42C:hardeningfresh-water -2.692e-03
## temperature42C:hardeningfresh-water-temperature -2.209e-03
## temperature42C:hardeningimmune -5.516e-03
## temperature42C:hardeningtemperature -3.213e-03
## temperature42C:final.mortalitydead -3.110e-04
## hardeningfresh-water:final.mortalitydead -1.244e-03
## hardeningfresh-water-temperature:final.mortalitydead -1.575e-03
## hardeningimmune:final.mortalitydead -2.164e-03
## hardeningtemperature:final.mortalitydead -1.723e-03
## temperature42C:hardeningfresh-water:final.mortalitydead 2.875e-03
## temperature42C:hardeningfresh-water-temperature:final.mortalitydead 2.304e-03
## temperature42C:hardeningimmune:final.mortalitydead 4.095e-03
## temperature42C:hardeningtemperature:final.mortalitydead 3.231e-03
## Std. Error
## (Intercept) 7.205e-04
## temperature42C 7.619e-04
## hardeningfresh-water 1.057e-03
## hardeningfresh-water-temperature 1.069e-03
## hardeningimmune 1.092e-03
## hardeningtemperature 1.061e-03
## final.mortalitydead 7.166e-04
## temperature42C:hardeningfresh-water 1.249e-03
## temperature42C:hardeningfresh-water-temperature 1.145e-03
## temperature42C:hardeningimmune 1.164e-03
## temperature42C:hardeningtemperature 1.465e-03
## temperature42C:final.mortalitydead 1.046e-03
## hardeningfresh-water:final.mortalitydead 1.104e-03
## hardeningfresh-water-temperature:final.mortalitydead 1.102e-03
## hardeningimmune:final.mortalitydead 1.258e-03
## hardeningtemperature:final.mortalitydead 1.130e-03
## temperature42C:hardeningfresh-water:final.mortalitydead 1.656e-03
## temperature42C:hardeningfresh-water-temperature:final.mortalitydead 1.583e-03
## temperature42C:hardeningimmune:final.mortalitydead 1.687e-03
## temperature42C:hardeningtemperature:final.mortalitydead 1.833e-03
## df
## (Intercept) 6.245e+00
## temperature42C 3.841e+02
## hardeningfresh-water 7.224e+00
## hardeningfresh-water-temperature 7.575e+00
## hardeningimmune 8.240e+00
## hardeningtemperature 7.353e+00
## final.mortalitydead 3.837e+02
## temperature42C:hardeningfresh-water 3.836e+02
## temperature42C:hardeningfresh-water-temperature 3.841e+02
## temperature42C:hardeningimmune 3.836e+02
## temperature42C:hardeningtemperature 3.834e+02
## temperature42C:final.mortalitydead 3.850e+02
## hardeningfresh-water:final.mortalitydead 3.841e+02
## hardeningfresh-water-temperature:final.mortalitydead 3.852e+02
## hardeningimmune:final.mortalitydead 3.846e+02
## hardeningtemperature:final.mortalitydead 3.843e+02
## temperature42C:hardeningfresh-water:final.mortalitydead 3.845e+02
## temperature42C:hardeningfresh-water-temperature:final.mortalitydead 3.863e+02
## temperature42C:hardeningimmune:final.mortalitydead 3.850e+02
## temperature42C:hardeningtemperature:final.mortalitydead 3.841e+02
## t value
## (Intercept) 11.320
## temperature42C -2.864
## hardeningfresh-water 1.340
## hardeningfresh-water-temperature 0.699
## hardeningimmune 4.139
## hardeningtemperature 2.416
## final.mortalitydead 1.890
## temperature42C:hardeningfresh-water -2.155
## temperature42C:hardeningfresh-water-temperature -1.930
## temperature42C:hardeningimmune -4.738
## temperature42C:hardeningtemperature -2.194
## temperature42C:final.mortalitydead -0.297
## hardeningfresh-water:final.mortalitydead -1.127
## hardeningfresh-water-temperature:final.mortalitydead -1.428
## hardeningimmune:final.mortalitydead -1.720
## hardeningtemperature:final.mortalitydead -1.524
## temperature42C:hardeningfresh-water:final.mortalitydead 1.736
## temperature42C:hardeningfresh-water-temperature:final.mortalitydead 1.456
## temperature42C:hardeningimmune:final.mortalitydead 2.427
## temperature42C:hardeningtemperature:final.mortalitydead 1.762
## Pr(>|t|)
## (Intercept) 2.15e-05
## temperature42C 0.00441
## hardeningfresh-water 0.22074
## hardeningfresh-water-temperature 0.50539
## hardeningimmune 0.00305
## hardeningtemperature 0.04474
## final.mortalitydead 0.05947
## temperature42C:hardeningfresh-water 0.03180
## temperature42C:hardeningfresh-water-temperature 0.05437
## temperature42C:hardeningimmune 3.04e-06
## temperature42C:hardeningtemperature 0.02886
## temperature42C:final.mortalitydead 0.76632
## hardeningfresh-water:final.mortalitydead 0.26025
## hardeningfresh-water-temperature:final.mortalitydead 0.15405
## hardeningimmune:final.mortalitydead 0.08619
## hardeningtemperature:final.mortalitydead 0.12835
## temperature42C:hardeningfresh-water:final.mortalitydead 0.08336
## temperature42C:hardeningfresh-water-temperature:final.mortalitydead 0.14633
## temperature42C:hardeningimmune:final.mortalitydead 0.01568
## temperature42C:hardeningtemperature:final.mortalitydead 0.07878
##
## (Intercept) ***
## temperature42C **
## hardeningfresh-water
## hardeningfresh-water-temperature
## hardeningimmune **
## hardeningtemperature *
## final.mortalitydead .
## temperature42C:hardeningfresh-water *
## temperature42C:hardeningfresh-water-temperature .
## temperature42C:hardeningimmune ***
## temperature42C:hardeningtemperature *
## temperature42C:final.mortalitydead
## hardeningfresh-water:final.mortalitydead
## hardeningfresh-water-temperature:final.mortalitydead
## hardeningimmune:final.mortalitydead .
## hardeningtemperature:final.mortalitydead
## temperature42C:hardeningfresh-water:final.mortalitydead .
## temperature42C:hardeningfresh-water-temperature:final.mortalitydead
## temperature42C:hardeningimmune:final.mortalitydead *
## temperature42C:hardeningtemperature:final.mortalitydead .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(model3)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF
## temperature 0.00097162 0.00097162 1 383.18
## hardening 0.00003400 0.00000850 4 5.59
## final.mortality 0.00008202 0.00008202 1 383.36
## temperature:hardening 0.00009415 0.00002354 4 383.19
## temperature:final.mortality 0.00007901 0.00007901 1 384.95
## hardening:final.mortality 0.00000298 0.00000075 4 383.33
## temperature:hardening:final.mortality 0.00003893 0.00000973 4 385.01
## F value Pr(>F)
## temperature 180.3584 < 2.2e-16 ***
## hardening 1.5779 0.3003121
## final.mortality 15.2248 0.0001127 ***
## temperature:hardening 4.3691 0.0018203 **
## temperature:final.mortality 14.6666 0.0001497 ***
## hardening:final.mortality 0.1384 0.9679863
## temperature:hardening:final.mortality 1.8068 0.1267407
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1rand(model3)## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## sqrt(value.mm3) ~ temperature + hardening + final.mortality + (1 | hardening:bag) + temperature:hardening + temperature:final.mortality + hardening:final.mortality + temperature:hardening:final.mortality
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 22 1770.1 -3496.2
## (1 | hardening:bag) 21 1762.0 -3481.9 16.345 1 5.279e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1qqPlot(residuals(model3))
## [1] 74 121Significant effects of temperature x hardening and temperature x mortality. Metabolic rate depending on mortality is not different between hardening treatments (no hardening x mortality).
Plot data
Plot mean response for each hardening treatment at 18°C and 42°C between oysters that ended up alive and dead by the end of the trial.
Plot first with individual points.
plot5<-final%>%
ggplot(aes(x=hardening, y=value.mm3, color=final.mortality))+
facet_grid(~temperature)+
geom_boxplot(position=position_dodge(0.5))+
geom_point(alpha=0.5, position=position_dodge(0.5))+
scale_colour_manual(values=c("darkgray", "darkred"))+
theme_classic()+
xlab("Hardening Treatment");plot5
plot5a<-final%>%
ggplot(aes(x=hardening, y=value.mm3, color=temperature))+
facet_grid(~final.mortality)+
geom_boxplot(position=position_dodge(0.9))+
geom_point(alpha=0.5, position=position_dodge(0.9))+
scale_colour_manual(values=c("cyan4", "orange"))+
theme_classic()+
xlab("Temperature");plot5a
plot5b<-final%>%
ggplot(aes(x=final.mortality, y=value.mm3, color=temperature))+
facet_grid(~hardening)+
geom_boxplot(position=position_dodge(0.9))+
geom_point(alpha=0.5, position=position_dodge(0.9))+
scale_colour_manual(values=c("cyan4", "orange"))+
theme_classic()+
xlab("Final Mortality");plot5b
Next plot with mean and sem for each group.
plot6<-final%>%
group_by(hardening, final.mortality, temperature)%>%
summarise(mean=mean(value.mm3, na.rm=TRUE), se=sd(value.mm3, na.rm=TRUE)/sqrt(length(value.mm3)))%>%
ggplot(aes(x=hardening, y=mean, color=final.mortality))+
facet_grid(~temperature)+
geom_errorbar(aes(ymin=mean-se, ymax=mean+se), width=0.1, position=position_dodge(0.5))+
geom_point(alpha=0.5, position=position_dodge(0.5))+
scale_colour_manual(values=c("darkgray", "darkred"))+
theme_classic()+
xlab("Hardening Treatment");plot6
plot6a<-final%>%
group_by(hardening, final.mortality, temperature)%>%
summarise(mean=mean(value.mm3, na.rm=TRUE), se=sd(value.mm3, na.rm=TRUE)/sqrt(length(value.mm3)))%>%
ggplot(aes(x=hardening, y=mean, color=temperature))+
facet_grid(~final.mortality)+
geom_point(alpha=0.5, position=position_dodge(0.9))+
geom_errorbar(aes(ymin=mean-se, ymax=mean+se), width=0.1, position=position_dodge(0.9))+
scale_colour_manual(values=c("cyan4", "orange"))+
theme_classic()+
xlab("Hardening");plot6a
plot6b<-final%>%
group_by(hardening, final.mortality, temperature)%>%
summarise(mean=mean(value.mm3, na.rm=TRUE), se=sd(value.mm3, na.rm=TRUE)/sqrt(length(value.mm3)))%>%
ggplot(aes(x=final.mortality, y=mean, color=temperature))+
facet_grid(~hardening)+
geom_line(aes(group=temperature), position=position_dodge(0.9))+
geom_point(alpha=0.5, position=position_dodge(0.9))+
geom_errorbar(aes(ymin=mean-se, ymax=mean+se), width=0.1, position=position_dodge(0.9))+
scale_colour_manual(values=c("cyan4", "orange"))+
theme_classic()+
xlab("Final Mortality");plot6b
Conduct posthoc tests
Effects of mortality within temperature and hardening treatment
anova(model3)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF
## temperature 0.00097162 0.00097162 1 383.18
## hardening 0.00003400 0.00000850 4 5.59
## final.mortality 0.00008202 0.00008202 1 383.36
## temperature:hardening 0.00009415 0.00002354 4 383.19
## temperature:final.mortality 0.00007901 0.00007901 1 384.95
## hardening:final.mortality 0.00000298 0.00000075 4 383.33
## temperature:hardening:final.mortality 0.00003893 0.00000973 4 385.01
## F value Pr(>F)
## temperature 180.3584 < 2.2e-16 ***
## hardening 1.5779 0.3003121
## final.mortality 15.2248 0.0001127 ***
## temperature:hardening 4.3691 0.0018203 **
## temperature:final.mortality 14.6666 0.0001497 ***
## hardening:final.mortality 0.1384 0.9679863
## temperature:hardening:final.mortality 1.8068 0.1267407
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1emm<-emmeans(model3, ~final.mortality|temperature|hardening, adjust = "tukey")
pairs(emm)## temperature = 18C, hardening = control:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.001355 0.000717 384 -1.890 0.0596
##
## temperature = 42C, hardening = control:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.001044 0.000755 384 -1.382 0.1678
##
## temperature = 18C, hardening = fresh-water:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.000110 0.000840 384 -0.131 0.8956
##
## temperature = 42C, hardening = fresh-water:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.002675 0.000969 383 -2.760 0.0061
##
## temperature = 18C, hardening = fresh-water-temperature:
## contrast estimate SE df t.ratio p.value
## alive - dead 0.000220 0.000840 386 0.262 0.7934
##
## temperature = 42C, hardening = fresh-water-temperature:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.001773 0.000828 385 -2.141 0.0329
##
## temperature = 18C, hardening = immune:
## contrast estimate SE df t.ratio p.value
## alive - dead 0.000810 0.001035 385 0.782 0.4347
##
## temperature = 42C, hardening = immune:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.002975 0.000823 383 -3.616 0.0003
##
## temperature = 18C, hardening = temperature:
## contrast estimate SE df t.ratio p.value
## alive - dead 0.000368 0.000875 385 0.421 0.6743
##
## temperature = 42C, hardening = temperature:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.002552 0.001225 383 -2.083 0.0379
##
## Note: contrasts are still on the sqrt scale
## Degrees-of-freedom method: kenward-rogerSignificant effects:
- Fresh water at 42°C had higher rates if the oyster died
- Fresh water temperature at 42°C had higher rates if the oyster died
- Immune at 42°C had higher rates if the oyster died
- Tempreature at 42°C had higher rates if oysters died
Control oysters did NOT have higher metabolic rates if the oyster died. No difference in alive vs dead oysters at 18°C.
Model mortality effects at time final for 18°C oysters
Detect outliers
Build a model including all predictors.
final_18C<-data%>%
filter(time==4)%>%
filter(temperature=="18C")
model4<-lmer(sqrt(value.mm3) ~ hardening * final.mortality + (1|hardening:bag), data=final_18C)
qqPlot(residuals(model4))
## [1] 78 35hist(final_18C$value.mm3)
Identify using standardized residuals.
# Extract raw residuals
final_18C$raw_resid <- residuals(model4)
# Standardize residuals
final_18C$std_resid <- final_18C$raw_resid / sd(final_18C$raw_resid)
# Flag potential outliers
outlier_threshold <- 3
final_18C$outlier_flag <- abs(final_18C$std_resid) > outlier_threshold
# Filter rows flagged as outliers
outliers <- final_18C %>% filter(outlier_flag == TRUE)
print(outliers)## # A tibble: 0 × 16
## # Groups: date, bag, sample, width.mm, length.mm [0]
## # ℹ 16 variables: date <dbl>, bag <dbl>, sample <chr>, hardening <chr>,
## # temperature <chr>, time <fct>, status <dbl>, width.mm <dbl>,
## # length.mm <dbl>, final.mortality <chr>, value <dbl>, volume.mm3 <dbl>,
## # value.mm3 <dbl>, raw_resid <dbl>, std_resid <dbl>, outlier_flag <lgl># Plot standardized residuals
ggplot(final_18C, aes(x = seq_along(std_resid), y = std_resid)) +
geom_point(aes(color = outlier_flag), size = 2) +
geom_hline(yintercept = c(-outlier_threshold, outlier_threshold), linetype = "dashed", color = "red") +
labs(title = "Standardized Residuals with Outliers", x = "Index", y = "Standardized Residual") +
theme_minimal()
No outliers detected.
hist(final_18C$value.mm3)
Analyze model
Plot raw data.
final_18C%>%
ggplot(aes(x=hardening, y=value.mm3, colour=final.mortality, group=sample))+
geom_point(position=position_dodge(0.5))+
theme_classic()
Analyze total change in fluorescence (fluorescence after 4 hours) and comparing those that ended up alive or dead at the end of the trial.
model4<-lmer(sqrt(value.mm3) ~ hardening * final.mortality + (1|hardening:bag), data=final_18C)
summary(model4)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(value.mm3) ~ hardening * final.mortality + (1 | hardening:bag)
## Data: final_18C
##
## REML criterion at convergence: -1582.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.07058 -0.58032 0.08023 0.70627 1.90661
##
## Random effects:
## Groups Name Variance Std.Dev.
## hardening:bag (Intercept) 2.560e-06 0.001600
## Residual 7.213e-06 0.002686
## Number of obs: 190, groups: hardening:bag, 10
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) 8.269e-03 1.208e-03
## hardeningfresh-water 1.281e-03 1.737e-03
## hardeningfresh-water-temperature 5.932e-04 1.748e-03
## hardeningimmune 4.390e-03 1.767e-03
## hardeningtemperature 2.567e-03 1.742e-03
## final.mortalitydead 1.455e-03 8.322e-04
## hardeningfresh-water:final.mortalitydead -1.245e-03 1.283e-03
## hardeningfresh-water-temperature:final.mortalitydead -1.159e-03 1.290e-03
## hardeningimmune:final.mortalitydead -2.107e-03 1.469e-03
## hardeningtemperature:final.mortalitydead -2.054e-03 1.316e-03
## df t value
## (Intercept) 4.709e+00 6.844
## hardeningfresh-water 5.036e+00 0.737
## hardeningfresh-water-temperature 5.156e+00 0.339
## hardeningimmune 5.382e+00 2.485
## hardeningtemperature 5.091e+00 1.473
## final.mortalitydead 1.755e+02 1.748
## hardeningfresh-water:final.mortalitydead 1.759e+02 -0.970
## hardeningfresh-water-temperature:final.mortalitydead 1.770e+02 -0.898
## hardeningimmune:final.mortalitydead 1.769e+02 -1.435
## hardeningtemperature:final.mortalitydead 1.761e+02 -1.561
## Pr(>|t|)
## (Intercept) 0.00129 **
## hardeningfresh-water 0.49374
## hardeningfresh-water-temperature 0.74769
## hardeningimmune 0.05205 .
## hardeningtemperature 0.19971
## final.mortalitydead 0.08213 .
## hardeningfresh-water:final.mortalitydead 0.33322
## hardeningfresh-water-temperature:final.mortalitydead 0.37023
## hardeningimmune:final.mortalitydead 0.15319
## hardeningtemperature:final.mortalitydead 0.12035
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) hrdnn- hrdn-- hrdnngm hrdnngt fnl.mr hrd-:. hr--:. hrdnngm:.
## hrdnngfrsh- -0.695
## hrdnngfrs-- -0.691 0.481
## hardenngmmn -0.684 0.476 0.473
## hrdnngtmprt -0.693 0.482 0.479 0.474
## fnl.mrtltyd -0.156 0.109 0.108 0.107 0.108
## hrdnngfr-:. 0.101 -0.197 -0.070 -0.069 -0.070 -0.648
## hrdnngf--:. 0.101 -0.070 -0.211 -0.069 -0.070 -0.645 0.418
## hrdnngmmn:. 0.088 -0.061 -0.061 -0.209 -0.061 -0.567 0.367 0.366
## hrdnngtmp:. 0.099 -0.069 -0.068 -0.067 -0.201 -0.632 0.410 0.408 0.358anova(model4)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## hardening 3.5313e-05 8.8283e-06 4 5.193 1.2240 0.4029
## final.mortality 7.1000e-07 7.1040e-07 1 176.893 0.0985 0.7540
## hardening:final.mortality 2.4024e-05 6.0060e-06 4 176.783 0.8327 0.5060rand(model4)## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## sqrt(value.mm3) ~ hardening + final.mortality + (1 | hardening:bag) + hardening:final.mortality
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 12 791.22 -1558.5
## (1 | hardening:bag) 11 782.50 -1543.0 17.456 1 2.94e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1qqPlot(residuals(model4))
## [1] 78 35No significant effects.
Plot data
Plot mean response for each hardening treatment between oysters that ended up alive and dead by the end of the trial at 18°C.
Plot first with individual points.
plot7<-final_18C%>%
ggplot(aes(x=hardening, y=value.mm3, color=final.mortality))+
geom_boxplot(position=position_dodge(0.5))+
geom_point(alpha=0.5, position=position_dodge(0.5))+
scale_colour_manual(values=c("darkgray", "darkred"))+
theme_classic()+
xlab("Hardening Treatment");plot7
plot7a<-final_18C%>%
ggplot(aes(x=temperature, y=value.mm3, color=hardening))+
geom_boxplot(position=position_dodge(0.9))+
geom_point(alpha=0.5, position=position_dodge(0.9))+
theme_classic()+
xlab("Temperature");plot7a
Next plot with mean and sem for each group.
plot8<-final_18C%>%
group_by(hardening, final.mortality)%>%
summarise(mean=mean(value.mm3, na.rm=TRUE), se=sd(value.mm3, na.rm=TRUE)/sqrt(length(value.mm3)))%>%
ggplot(aes(x=hardening, y=mean, color=final.mortality))+
geom_errorbar(aes(ymin=mean-se, ymax=mean+se), width=0.1, position=position_dodge(0.5))+
geom_point(alpha=0.5, position=position_dodge(0.5))+
scale_colour_manual(values=c("darkgray", "darkred"))+
theme_classic()+
xlab("Hardening Treatment");plot8
plot8a<-final_18C%>%
group_by(hardening, final.mortality)%>%
summarise(mean=mean(value.mm3, na.rm=TRUE), se=sd(value.mm3, na.rm=TRUE)/sqrt(length(value.mm3)))%>%
ggplot(aes(x=final.mortality, y=mean, color=hardening))+
geom_errorbar(aes(ymin=mean-se, ymax=mean+se), width=0.1, position=position_dodge(0.1))+
geom_point(alpha=0.5, position=position_dodge(0.1))+
geom_line(aes(group=hardening))+
theme_classic()+
xlab("Final Mortality");plot8a
Conduct posthoc tests
Effects of mortality within hardening treatment
anova(model4)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## hardening 3.5313e-05 8.8283e-06 4 5.193 1.2240 0.4029
## final.mortality 7.1000e-07 7.1040e-07 1 176.893 0.0985 0.7540
## hardening:final.mortality 2.4024e-05 6.0060e-06 4 176.783 0.8327 0.5060emm<-emmeans(model4, ~final.mortality|hardening, adjust = "tukey")
pairs(emm)## hardening = control:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.001455 0.000833 176 -1.747 0.0824
##
## hardening = fresh-water:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.000210 0.000978 176 -0.215 0.8304
##
## hardening = fresh-water-temperature:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.000296 0.000990 178 -0.299 0.7650
##
## hardening = immune:
## contrast estimate SE df t.ratio p.value
## alive - dead 0.000652 0.001214 177 0.537 0.5919
##
## hardening = temperature:
## contrast estimate SE df t.ratio p.value
## alive - dead 0.000599 0.001021 177 0.586 0.5584
##
## Note: contrasts are still on the sqrt scale
## Degrees-of-freedom method: kenward-rogerNo differences.
Model mortality effects at time final for 42°C oysters
Detect outliers
Build a model including all predictors.
final_42C<-data%>%
filter(time==4)%>%
filter(temperature=="42C")
model5<-lmer(sqrt(value.mm3) ~ hardening * final.mortality + (1|hardening:bag), data=final_42C)
qqPlot(residuals(model5))
## [1] 54 115hist(final_42C$value.mm3)
Identify using standardized residuals.
# Extract raw residuals
final_42C$raw_resid <- residuals(model5)
# Standardize residuals
final_42C$std_resid <- final_42C$raw_resid / sd(final_42C$raw_resid)
# Flag potential outliers
outlier_threshold <- 3
final_42C$outlier_flag <- abs(final_42C$std_resid) > outlier_threshold
# Filter rows flagged as outliers
outliers <- final_42C %>% filter(outlier_flag == TRUE)
print(outliers)## # A tibble: 0 × 16
## # Groups: date, bag, sample, width.mm, length.mm [0]
## # ℹ 16 variables: date <dbl>, bag <dbl>, sample <chr>, hardening <chr>,
## # temperature <chr>, time <fct>, status <dbl>, width.mm <dbl>,
## # length.mm <dbl>, final.mortality <chr>, value <dbl>, volume.mm3 <dbl>,
## # value.mm3 <dbl>, raw_resid <dbl>, std_resid <dbl>, outlier_flag <lgl># Plot standardized residuals
ggplot(final_42C, aes(x = seq_along(std_resid), y = std_resid)) +
geom_point(aes(color = outlier_flag), size = 2) +
geom_hline(yintercept = c(-outlier_threshold, outlier_threshold), linetype = "dashed", color = "red") +
labs(title = "Standardized Residuals with Outliers", x = "Index", y = "Standardized Residual") +
theme_minimal()
hist(final_42C$value.mm3)
Analyze model
Plot raw data.
final_42C%>%
ggplot(aes(x=hardening, y=value.mm3, colour=final.mortality, group=sample))+
geom_point(position=position_dodge(0.5))+
theme_classic()
Analyze total change in fluorescence (fluorescence after 4 hours) and comparing those that ended up alive or dead at the end of the trial.
model5<-lmer(sqrt(value.mm3) ~ hardening * final.mortality + (1|hardening:bag), data=final_42C)
summary(model5)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(value.mm3) ~ hardening * final.mortality + (1 | hardening:bag)
## Data: final_42C
##
## REML criterion at convergence: -2000.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.59081 -0.61084 -0.03183 0.64516 2.83816
##
## Random effects:
## Groups Name Variance Std.Dev.
## hardening:bag (Intercept) 3.425e-07 0.0005853
## Residual 3.312e-06 0.0018200
## Number of obs: 218, groups: hardening:bag, 10
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) 5.750e-03 6.841e-04
## hardeningfresh-water -1.064e-03 1.055e-03
## hardeningfresh-water-temperature -1.459e-03 9.719e-04
## hardeningimmune -7.922e-04 9.700e-04
## hardeningtemperature -4.245e-04 1.211e-03
## final.mortalitydead 1.184e-03 5.942e-04
## hardeningfresh-water:final.mortalitydead 1.504e-03 9.649e-04
## hardeningfresh-water-temperature:final.mortalitydead 8.946e-04 8.812e-04
## hardeningimmune:final.mortalitydead 1.820e-03 8.771e-04
## hardeningtemperature:final.mortalitydead 1.356e-03 1.130e-03
## df t value
## (Intercept) 1.537e+01 8.405
## hardeningfresh-water 2.206e+01 -1.009
## hardeningfresh-water-temperature 1.602e+01 -1.501
## hardeningimmune 1.600e+01 -0.817
## hardeningtemperature 3.665e+01 -0.350
## final.mortalitydead 2.060e+02 1.992
## hardeningfresh-water:final.mortalitydead 2.044e+02 1.559
## hardeningfresh-water-temperature:final.mortalitydead 2.060e+02 1.015
## hardeningimmune:final.mortalitydead 2.046e+02 2.075
## hardeningtemperature:final.mortalitydead 2.038e+02 1.200
## Pr(>|t|)
## (Intercept) 3.9e-07 ***
## hardeningfresh-water 0.3241
## hardeningfresh-water-temperature 0.1528
## hardeningimmune 0.4261
## hardeningtemperature 0.7280
## final.mortalitydead 0.0477 *
## hardeningfresh-water:final.mortalitydead 0.1205
## hardeningfresh-water-temperature:final.mortalitydead 0.3112
## hardeningimmune:final.mortalitydead 0.0392 *
## hardeningtemperature:final.mortalitydead 0.2314
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) hrdnn- hrdn-- hrdnngm hrdnngt fnl.mr hrd-:. hr--:. hrdnngm:.
## hrdnngfrsh- -0.648
## hrdnngfrs-- -0.704 0.456
## hardenngmmn -0.705 0.457 0.496
## hrdnngtmprt -0.565 0.366 0.398 0.398
## fnl.mrtltyd -0.711 0.461 0.500 0.501 0.401
## hrdnngfr-:. 0.438 -0.750 -0.308 -0.309 -0.247 -0.616
## hrdnngf--:. 0.479 -0.311 -0.696 -0.338 -0.271 -0.674 0.415
## hrdnngmmn:. 0.482 -0.312 -0.339 -0.694 -0.272 -0.677 0.417 0.457
## hrdnngtmp:. 0.374 -0.242 -0.263 -0.264 -0.816 -0.526 0.324 0.355 0.356anova(model5)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## hardening 1.1444e-05 2.8610e-06 4 6.641 0.8638 0.5316
## final.mortality 1.6247e-04 1.6247e-04 1 204.003 49.0501 3.546e-11
## hardening:final.mortality 1.6724e-05 4.1810e-06 4 204.266 1.2623 0.2861
##
## hardening
## final.mortality ***
## hardening:final.mortality
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1rand(model5)## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## sqrt(value.mm3) ~ hardening + final.mortality + (1 | hardening:bag) + hardening:final.mortality
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 12 1000.1 -1976.3
## (1 | hardening:bag) 11 998.0 -1974.0 4.2811 1 0.03854 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1qqPlot(residuals(model5))
## [1] 54 115Significant effect of mortality on metabolic rates at 42°C.
Plot data
Plot mean response for each hardening treatment between oysters that ended up alive and dead by the end of the trial at 18°C.
Plot first with individual points.
plot9<-final_42C%>%
ggplot(aes(x=hardening, y=value.mm3, color=final.mortality))+
geom_boxplot(position=position_dodge(0.5))+
geom_point(alpha=0.5, position=position_dodge(0.5))+
scale_colour_manual(values=c("darkgray", "darkred"))+
theme_classic()+
xlab("Hardening Treatment");plot9
plot9a<-final_42C%>%
ggplot(aes(x=temperature, y=value.mm3, color=hardening))+
geom_boxplot(position=position_dodge(0.9))+
geom_point(alpha=0.5, position=position_dodge(0.9))+
theme_classic()+
xlab("Temperature");plot9a
Next plot with mean and sem for each group.
plot9<-final_42C%>%
group_by(hardening, final.mortality)%>%
summarise(mean=mean(value.mm3, na.rm=TRUE), se=sd(value.mm3, na.rm=TRUE)/sqrt(length(value.mm3)))%>%
ggplot(aes(x=hardening, y=mean, color=final.mortality))+
geom_errorbar(aes(ymin=mean-se, ymax=mean+se), width=0.1, position=position_dodge(0.5))+
geom_point(alpha=0.5, position=position_dodge(0.5))+
scale_colour_manual(values=c("darkgray", "darkred"))+
theme_classic()+
xlab("Hardening Treatment");plot9
plot9a<-final_42C%>%
group_by(hardening, final.mortality)%>%
summarise(mean=mean(value.mm3, na.rm=TRUE), se=sd(value.mm3, na.rm=TRUE)/sqrt(length(value.mm3)))%>%
ggplot(aes(x=final.mortality, y=mean, color=hardening))+
geom_errorbar(aes(ymin=mean-se, ymax=mean+se), width=0.1, position=position_dodge(0.1))+
geom_point(alpha=0.5, position=position_dodge(0.1))+
geom_line(aes(group=hardening), position=position_dodge(0.1))+
theme_classic()+
xlab("Final Mortality");plot9a
Conduct posthoc tests
Effects of mortality within hardening treatment
anova(model5)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## hardening 1.1444e-05 2.8610e-06 4 6.641 0.8638 0.5316
## final.mortality 1.6247e-04 1.6247e-04 1 204.003 49.0501 3.546e-11
## hardening:final.mortality 1.6724e-05 4.1810e-06 4 204.266 1.2623 0.2861
##
## hardening
## final.mortality ***
## hardening:final.mortality
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1emm<-emmeans(model5, ~final.mortality|hardening, adjust = "tukey")
pairs(emm)## hardening = control:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.00118 0.000597 206 -1.984 0.0486
##
## hardening = fresh-water:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.00269 0.000760 203 -3.535 0.0005
##
## hardening = fresh-water-temperature:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.00208 0.000653 206 -3.182 0.0017
##
## hardening = immune:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.00300 0.000645 203 -4.654 <.0001
##
## hardening = temperature:
## contrast estimate SE df t.ratio p.value
## alive - dead -0.00254 0.000961 203 -2.644 0.0088
##
## Note: contrasts are still on the sqrt scale
## Degrees-of-freedom method: kenward-rogerAll treatments have higher metabolic rates in oysters that died at 42°C (control is P=0.05 when rounded).